Designing minimum-cost networks that are robust and avoid obstacles

这个项目的目标是构建一个数学框架，用于设计健壮且避开障碍的最低成本网络。物理网络，如通信、电力和交通所需的网络，对我们的社会至关重要，但从经济和环境角度来看，成本高昂。需要数学优化工具来设计考虑到实际考虑的最低成本网络，例如在本地连接故障中幸存下来并避免预先存在的障碍。这些都被认为是具有数学挑战性的问题。当前的方法使用的限制性模型没有抓住现代基础设施网络的灵活性。该项目旨在开发使用可变的‘Steiner点’的几何设计方法，导致快速算法来优化解决这些问题。

The goal of this project is to construct a mathematical framework for the design of minimum-cost networks that are robust and avoid obstacles. Physical networks such as those required for communication, power and transportation are vital for our society, but are costly from economic and environmental viewpoints. There is a need for mathematical optimisation tools to design minimum-cost networks that take into account practical considerations such as surviving local connectivity failures and avoiding pre-existing obstacles. These are recognised as mathematically challenging problems. Current approaches employ restrictive models that do not capture the flexibility of modern infrastructure networks. This project aims to develop geometric design methods using variable ‘Steiner points’, leading to fast algorithms for optimally solving these problems.